Clear air turbulence (CAT) is a major safety concern for large commercial aircraft. CAT is a weather phenomenon that is associated with vertical wind shear and stable layers in the atmosphere. CAT results in a rapidly changing airflow over the lift surfaces of the aircraft. Should the forward velocity of the air over the lift surfaces suddenly decrease, the lift will decrease. In this situation, the aircraft may experience a forced descent due to the down flowing air mass and also by an apparent loss in forward air speed. It is thus desirable that an onboard weather system be capable of providing an advanced warning of such wind conditions.
Since the conditions that result in clear air turbulence are not visually apparent nor are they generally detectable by active sensors such as radar, there have been a number of attempts to detect wind shear and clear air turbulence conditions by passive detectors. In particular, attempts have been made to sense air temperature gradients, which are associated with air turbulence, by detecting the radiation emanating from the atmosphere ahead of the aircraft in the infrared and microwave spectral regions. The intensity of the detected radiation varies with the atmospheric temperatures along the line of sight of the detector. Typically these passive systems use a radiometer to measure the thermal radiation from one of the atmospheric gases such as carbon dioxide (CO.sub.2), oxygen (O.sub.2) or water vapor (H.sub.2 O) to determine changes in the spatial temperature profile in front of the aircraft. Examples of such approaches based on the infrared emission of CO.sub.2 are provided in U.S. Pat. Nos. 3,475,963, 3,735,136, 3,780,293, 3,935,460, 4,266,130, 4,427,306, 4,937,447, 4,965,572, 4,965,573, 5,105,191, 5,276,326 and 5,285,070. Other approaches determine atmospheric temperature by measuring the microwave emission from O.sub.2 as described in U.S. Pat. Nos. 3,359,557, 3,380,055, 4,346,595, and 5,117,689. Systems for measuring atmospheric temperature based on infrared emission from H.sub.2 O are described in U.S. Pat. No. 4,266,130 and in the paper by Kuhn et al, "Clear Air Turbulence: Detection by Infrared Observations of Water Vapor" in Science, Vol. 196, p. 1099, (1977). In addition, there have been several papers written describing these types of passive infrared systems including: S. M. Norman and N. H. Macoy, "Remote Detection of Clear Air Turbulence by Means of an Airborne Infrared System" AJAA Paper No. 65-459 presented at the AIAA Second Annual Meeting, San Francisco, Calif., Jul. 26-29, 1965; and R. W. Astheimer, "The Remote Detection of Clear Air Turbulence by Infrared Radiation" in Applied Optics Vol. 9, No. 8, p. 1789 (1970). In U.S. Pat. No. 4,346,595, Gary describes a microwave radiometer for determining air temperatures in the atmosphere at ranges of about 3 km from the aircraft for the purpose of detecting the height of the tropopause and the presence of temperature inversions. He teaches that by flying the aircraft above or below the tropopause or temperature inversion layer, it is possible to avoid CAT. Since the effective range of the microwave radiometer is relatively short, the system doesn't provide sufficient warning time for the aircraft to avoid the CAT condition. The present invention has detection ranges on the order of 100 km which will allow time for the aircraft to change altitude to avoid CAT.
A number of the above systems were not successful or were only partially successful because they were based solely on the measurement of atmospheric temperature in order to predict the presence of turbulence. A more reliable indication of atmospheric turbulence can be realized by determining the Richardson number, Ri. The use of the Richardson number to determine the stability of the atmosphere is well known in meteorology (see, for example, D. Djuric, Weather Analysis, Prentice Hall, Englewood Cliffs, N.J., 1994, p. 64). In the present invention, the Richardson number is used to indicate the probability of CAT. In U.S. Pat. No. 5,117,689, Gary discussed the correlation of the reciprocal of the Richardson number with the occurrence of CAT conditions.
The Richardson number contains two components: (1) the vertical lapse rate of potential temperature and (2) the wind shear which is related to the horizontal temperature gradient. A number of the prior art discussions measure the vertical temperature lapse rate. Gary used the inertial navigation system (INS) to measure the East-West and North-South components of the wind to calculate the wind shear along with a microwave radiometer to measure the air temperature vertical lapse rate. This information is then used to calculate the Richardson number or its reciprocal. The deficiency of the system described in this patent (U.S. Pat. No. 5,117,689) is that it determines the Richardson number at relatively close ranges (less than 3 km) and therefore does not provide advance warning of the CAT condition and that it measures the wind shear only at the aircraft.
Previous approaches for the determination of the range and probability of CAT can be summarized as follows:
U.S. Pat. No. 5,276,326 to Philpott determines turbulence as a function of temperature vs. range through the analysis of infrared radiometer signals at two or more discrete wavelengths. The temperature associated with a given range as a function of wavelength is then derived through a matrix inversion process. This transition is difficult and requires noise and error free input data to yield valid results. The present invention overcomes this difficulty by using only one wavelength. Gary overcomes the multiple wavelength difficulty in U.S. Pat. No. 4,346,595 by measuring effective temperature and range at a single wavelength, however no attempt is made to determine the probability of clear air turbulence using the Richardson number. In U.S. Pat. No. 5,117,689, Gary teaches the significance of the Richardson number in CAT prediction but does not suggest a method to derive Ri directly from radiometric measurements of horizontal and vertical temperature lapse rates obtained by combining azimuth and elevation scanning with the aircraft motion to produce a temperature map.
Since the early 60's several theoretical studies and field experiments have established a link between CAT and meso- and synoptic-scale dynamics. These scales range from 10's of km to 1000 km. The systems include jet streams in association with upper level frontogenesis, gravity waves, mountain waves and Kelvin-Helmholtz Instability (KHI).
Both theoretical studies and laboratory experiments have established the fundamental importance of the Richardson number to the onset of atmospheric turbulence. The Richardson number is defined as ##EQU1## where ##EQU2## and where .theta. is the potential temperature, .differential..theta./.differential.z is the vertical gradient of the potential temperature (defined as the lapse rate), .differential.V/.differential.z is the vertical wind shear, g is acceleration due to gravity, T is temperature in Kelvin, p is atmospheric pressure in millibars, R is the universal gas constant and C.sub.p is the specific heat of air at constant pressure. The studies by W. T. Roach ("On the influence of synoptic development on the production of high level turbulence," Quart. J. R. Met. Soc., (1970) 96, 413), J. L. Keller ("Clear Air Turbulence as a Response to Meso- and Synoptic-Scale Dynamic Processes," Monthly Weather Review, (1990) 118, 2228), both incorporated by reference herein, and others have concluded that although CAT occurs at unresolvable subgrid scales, the energy dissipation rate due to CAT may be determined by resolvable, gridscale dynamical processes. Roach and Keller, in particular, showed that the total Ri tendency, .GAMMA., which is defined as the time rate of change of ln(Ri) following the motion, may be divided into nonturbulent and turbulent components, such that ##EQU3##
The nonturbulent component, .PHI., is a result of shearing and stretching deformations associated with meso-alpha and synoptic scale disturbances in the upper troposphere. The processes acting to modify ln(Ri) and attributed to .xi. are due to the unresolvable subgrid phenomena associated with CAT; these include Kelvin-Helmholtz instabilities with horizontal scales of a few km and random turbulent eddies of a few tens or hundreds of meters. With existing monitoring equipment, measurement of Ri with an appropriate resolution is difficult. Instead, measurement techniques are more likely acquiring a spatial average of Ri. The layered Richardson number, Ri.sub.L, is the average of Ri over an atmospheric layer. It is defined as ##EQU4## where .DELTA.V/.DELTA.z and .DELTA..theta./.DELTA.z are the values of the vertical wind shear and potential temperature lapse rate, respectively, averaged over the atmospheric layer. Currently, Ri.sub.L is calculated from wind and temperature fields obtained from numerical forecast models. Input data for the models are from radiosonde, satellite and pilot reports. The key input data, from the radiosonde, have spatial resolution of approximately 300 km and temporal resolution of 12 hours. Over oceanic areas the spatial resolution is much worse.
An important outcome of the Roach and Keller studies is that the value of Ri.sub.L =1/2 appears to be the layered-averaged analog to the Miles-Howard critical value of Ri=1/4 which relates to the necessary condition for individual turbulent events. Another important outcome is a means to determine the rate at which energy is transformed from the nonturbulent meso scale to the turbulent scale. The rate, .epsilon., at which energy is transformed from the nonturbulent to the turbulent scale is given by ##EQU5## where .DELTA.v is the change in the horizontal wind speed between the bottom and top of the layer. Keller discloses the critical link between Ri.sub.L and Ri and how sustained turbulent layers may develop in the free atmosphere. As a parcel of atmosphere with an arbitrarily large Ri enters a region where .PHI.&gt;0, its Ri begins to decrease. If the parcel remains in this environment long enough, Ri will continue to decrease to the Miles-Howard critical value (Ri=1/4) necessary for Kelvin-Helmholtz instabilities and turbulence. Once turbulence occurs, vertical mixing would, after several minutes, increase Ri above 1/4. If the parcel remains in the same environment, its Ri once again decreases beginning the cycle anew. The process is repeated until the parcel enters a region where .PHI.&lt;0. While Ri would be varying dramatically over a short distance (on the order of 20 m), its variation averaged over a longer distance (100 m and up), Ri.sub.L,would be small. In addition, for the kinetic energy of the vertical shear to be available for transformation to the turbulent scale, the average Ri.sub.L =1/2 is necessary.
Other researchers have shown that it is possible to delineate quantitatively the components of turbulence energy. For example, Kennedy and Shapiro (P. J. Kennedy and M. A. Shapiro, "Further Encounters with Clear Air Turbulence in Research Aircraft," Journal of Atmospheric Sciences, (1980), 37, 986), incorporated by referenced herein, computed and accounted for the various terms in the turbulence energy budget.
An approximation of the turbulent kinetic energy is given by ##EQU6## where E is the turbulent kinetic energy (TKE), V is the wind vector, g is the gravitational acceleration, and .THETA..sub.o is the potential temperature. The angle braces indicate average over space of v, the horizontal velocity perturbation, w the vertical velocity perturbation, and .theta. the potential temperature perturbation. .epsilon. is the TKE dissipation, and the first two terms are the TKE production due to wind shear and stability respectively.
A simple approach of closing the TKE equation is by using the relation between the covariance of the perturbation quantities and the eddy diffusivities of momentum and heat, so that ##EQU7## where K.sub.M and K.sub.H are the eddy diffusivities for momentum and heat respectively.
An estimate of the dissipation, .epsilon., can be obtained from Eq. (6) by assuming a steady-state condition. For this case, the dissipation, .epsilon., equals the production. Solving Eq. (6) for .epsilon. yields ##EQU8## and the ratio of the eddy viscosity (K.sub.M) to the eddy thermal diffusivity (K.sub.H) is the turbulent Prandtl number (Pr).
Studies such as those outlined above have led to the development of a number of algorithms for predicting the probability of detection (POD) of CAT and the false alarm ratio (FAR). The results from using these algorithms, as indicated below, supports the idea that i) mesoscale parameters could be used to infer CAT activity; and ii) the POD and FAR are limited by the spatial, and in particular, the temporal resolutions currently available from radiosonde and numerical model forecasts.
The inputs to the algorithms are derived from various numerical forecast models, such as the nested grid model (NGM) or the global aviation model (AVN), which are produced twice daily (0000 and 1200 UTC) at the National Meteorological Center in Washington, DC. The horizontal resolution of the NGM, for example, is 85 to 90 km over North America, with vertical resolution of 16 layers. The thickness of each NGM layer varies from about 35 mb near the surface to a maximum of 75 mb in the midtroposphere (near 450 mb).
Verification statistics correlated with the algorithms show excellent objective ability to detect or forecast areas of turbulence. Probability of detection statistics indicates that about 75% of CAT events can be predicted. The false alarm ratios suggest a 1 in every 4 or 5 events will be incorrect, based on pilot reports (PIREPS) over the United States. These statistics are not unexpected, however, since the input data are based on 6 and 12 hour forecasts from the numerical models.
Whereas the above mentioned algorithms use the wind field to derive some of the key input parameters, the present invention uses the temperature field. The invention will allow the use of real time measurement of temperature as compared with the 6 hr to 12 hr forecast currently being used. In addition, the invention allows an aircraft (or arbitrary platform) to have the measurements centered at the aircraft. Finally, the invention permits horizontal scale measurements in the order of 10 km to 200 km, vertical scale measurement of between 100 and 500 meters, and temporal resolution on the order of minutes or less, a significant improvement over the current spatial and temporal resolutions.